He guarded the entrance of the ship, but was bored of his job. He rather liked to see the band Death by Solar Radiations on their last Earth gig than stopping people from entering the ship.
When the Doctor and Amy came back to the SS Lucy Gray centuries later the Doctor saw a holographic photo of Jason, revealing that his surname was Venezia. The photos were in a hallway together with a statue of Amy and the Doctor. (GAME: Return to Earth)